Nondiffracting Fields Research Articles

Generation of tightly focused twin Bessel beams using circular Dammann gratings under radial polarization incidence

Generation of longitudinally polarized focusing twin Bessel beams in focal region of a high numerical aperture (NA) objective is described based on circular Dammann gratings for radially polarized Bessel–Gauss input fields. Numerical simulations show that, under focusing of an objective of NA=0.95, the depth of focus (DOF) of the focused twin Bessel beams can reach as long as tens or even ∼102 of wavelengths while its average transverse spot over the whole range of the DOF is kept subdiffration-limited. At the same time, the longitudinal polarization purity in focus volume is higher than 90% for the central lobe. Therefore, this tightly focused non-diffracting field should be of great interest for applications in numerous areas, such as particle acceleration and manipulation, micromachining, second-harmonic generation, Raman spectroscopy, etc.

Holographic generation of a class of nondiffracting fields with optimum efficiency

We discuss the accurate generation of complex optical fields using phase holograms that provide the optimum diffraction efficiency. In each considered case, the phase modulation of the employed hologram is identical to the phase of the desired optical field. We show that periodic and quasiperiodic nondiffracting optical fields, mathematically obtained through the superposition of multiple plane waves, can be generated with high fidelity using this approach.

Controlling the evolution of nondiffracting speckle by complex amplitude modulation on a phase-only spatial light modulator

In this work we investigate the structure of nondiffracting speckle fields, both experimentally and theoretically. We are able to produce very good agreement between the experimentally recorded and theoretically calculated fields by using complex amplitude modulation on a phase-only spatial light modulator to implement controlled ring-slit experiments for the generation of nondiffracting speckle fields. The structure of the nondiffracting speckle due to binary and continuous phase modulations for both a uniform and a normal distribution is investigated. We find that we are able to engineer whether the nondiffracting field will appear as speckle or a structured zero-order Bessel beam by adjusting the standard deviation in the distribution. Having the ability to control where in the spectrum, from fully-developed nondiffracting speckle to a symmetric zero-order Bessel beam, the nondiffracting field will exist can prove to be a useful resource in the non-destructive testing of materials.

Increasing the structural variety of discrete nondiffracting wave fields

We investigate discrete nondiffracting beams (DNBs) being the foundation of periodic and quasiperiodic intensity distributions. Besides the number of interfering plane waves, the phase relation among these waves is decisive to form a particular intensity lattice. In this manner, we systematize different classes of DNBs and present similarities as well as differences. As one prominent instance, we introduce the class of sixfold nondiffracting beams, offering four entirely different transverse intensity distributions: in detail, the hexagonal, kagome, and honeycomb pattern, as well as a hexagonal vortex beam. We further extend our considerations to quasiperiodic structures and show the changeover to Bessel beams. In addition, we introduce a highly flexible implementation of the experimental analog of DNBs, namely discrete pseudo-nondiffracting beams, and present locally resolved intensity and phase measurements, which underline the nondiffracting character of the generated wave fields.

Periodic and quasi-periodic non-diffracting wave fields generated by superposition of multiple Bessel beams

We discuss a computer generated hologram whose transmittance is defined in terms of the Jacobi-Anger identity. If the hologram is implemented with a continuous phase spatial light modulator it generates integer-order non-diffracting Bessel beams, with a common asymptotic radial frequency, at separated propagation axes. On the other hand, when the hologram is implemented with a low-resolution pixelated phase modulator, it is possible to generate multiple Bessel beams with a common propagation axis. We employ this superposition of multiple Bessel beams to generate non-diffracting periodic and quasi-periodic wave fields.

Nondiffracting electromagnetic fields in inhomogeneous isotropic media

In this paper stationary nondiffracting vector fields are discussed. Using the definition of propagating and evanescent nondiffracting waves based on the invariance of the intensity distribution during propagation, all the types of such fields in stratified inhomogeneous media are found.

Observation of parabolic nondiffracting optical fields

We report the first experimental observation of parabolic non-diffracting beams, the fourth fundamental family of propagation-invariant optical fields of the Helmholtz equation. We generate the even and odd stationary parabolic beam and with them we are able to produce traveling parabolic beams. It is observed that these fields exhibit a number of unitary in-line vortices that do not interact on propagation. The experimental transverse patterns show an inherent parabolic structure in good agreement with the theoretical predictions. Our results exhibit a transverse energy flow of traveling beams never observed before.

Bessel beams: Diffraction in a new light

Diffraction is a cornerstone of optical physics and has implications for the design of all optical systems. The paper discusses the so-called 'non-diffracting' light field, commonly known as the Bessel beam. Approximations to such beams can be experimentally realized using a range of different means. The theoretical foundation of these beams is described and then various experiments that make use of Bessel beams are discussed: these cover a wide range of fields including non-linear optics, where the intense central core of the Bessel beam has attracted interest; short pulse non-diffracting fields; atom optics, where the narrow non-diffracting features of the Bessel beam are able to act as atomic guides and atomic confinement devices and optical manipulation, where the reconstruction properties of the beam enable new effects to be observed that cannot be seen with Gaussian beams. The intensity profile of the Bessel beam may offer routes to investigating statistical physics as well as new techniques for the optical sorting of particles.

Parabolic nondiffracting optical wave fields.

We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

Azimuthal polarization and partial coherence.

Partially coherent fields with the electric field parallel to the azimuthal coordinate are analyzed by use of the exact angular spectrum representation. The known results for fully coherent fields are used to find the permitted forms of azimuthally polarized, partially coherent fields. The derived result is then used to show that this class of fields is severely restricted because the azimuthal polarization state is particularly sensitive to the correlation properties of the electric-field components. Two examples of azimuthally polarized fields are briefly examined. The first is a class of nondiffracting fields that retain the polarization state upon propagation, whereas the second is an example in which the azimuthal polarization is broken because the cross-spectral density function is not of the permitted form.

Propagation-independent fields

Nondiffracting beams are solutions of the wave equation which keep their shape during free propagation. Because of this property, they are widely studied, both as mechanical and electromagnetic waves. Another scheme, however, can be devised in order to find beams that, even if do not maintain their shape upon propagation, are independent on the propagation distance, apart from a phase factor. In this sense it can be said that these beams are also nondiffracting. In this work, the scheme leading to this different kind of nondiffracting fields, which we term propagation-independent beams, is presented. Closed-form expressions for a few of these fields, for 1-D sources, are found. A method, which in principle is able to produce beams of this type, is given. This also clarifies some of their properties. Finally, the item of finite realizations of these beams, which in principle require infinite-dimension sources, is analyzed through numerical simulations. It is also shown that the practical feasibility of these fields poses some limitations on the bandwidth they can present.

Vectorial spectral analysis of the nonstationary electromagnetic field

A general concept of the vectorial spectral analysis of the nonstationary optical fields representing exact solutions to the Maxwell equations is proposed. The method provides the possibility of examining the free-space spatiotemporal evolution of the electromagnetic field in relation to its dependence on the composition of its temporal- and angular-frequency spectra. Particular attention is given to the electromagnetic pulses whose monochromatic components are nondiffracting fields.

Space-frequency analysis of nondiffracting pulses

A recently introduced method of producing nondiffracting space-time fields from ordinary diffracting solutions is here examined in the space-frequency domain. It is shown that in a 3D space the method leads to localized wavefields whose Fourier components are nondiffracting beams. Hence the nondiffracting pulses are spectral generalizations of the monochromatic conical waves, a property which provides novel insight into the physical analysis and the actual preparation of such localized space-time fields. In 2D, the resulting temporally varying wavefields are nonlocalized. The nondiffracting pulses obtained via the space-frequency synthesis of conical waves are illustrated with the help of broadband X waves and their temporal derivatives for which explicit expressions are derived. The relation of these fields to the previously known localized solutions is established.

Nondiffracting stationary electromagnetic field

A class of electromagnetic fields which are nondiffracting, in the sense of a given definition, is investigated. General stationary nondiffracting electromagnetic fields are constructed from solutions of the scalar Helmholtz equation. Some nondiffracting fields in cylindrical coordinates are investigated by means of properties of the transversal Poynting vector. It is shown that the amplitudes of the electric and magnetic vectors are, in the studied cases, proportional to the superposition of Bessel functions and the phases can have features of vector optical vortices (phases have edge and screw dislocations).

Nondiffractive fields.

At the present time no general definition of nondiffractive beam has been generally accepted. We propose one simple definition based on the Poynting vector and light intensity. \textcopyright{} 1996 The American Physical Society.

Stationary-phase analysis of generalized axicons

Simple asymptotic expressions based on diffraction and the method of stationary phase are derived for the axial line images produced by generalized axicons. It is shown that many of the previously numerically established results concerning the logarithmic uniform-intensity axicons readily follow from these expressions. The role of the radial and azimuthal hologram variations in axicon image formation is elucidated. In particular, the generation of hollow uniform-intensity axicon lines of finite length is demonstrated. Linear holographic axicons are shown to produce a uniform axial line of high transverse definition if the illumination intensity is suitably varied along the radial direction. The connection of axicon images with nondiffracting wave fields is also discussed.

Realization of general nondiffracting beams with computer-generated holograms.

A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.

Nondiffracting optical fields: some remarks on their analysis and synthesis

Recently Durnin pointed out the existence of nondiffracting beams that propagate in free space with their energy confined around their axis but that experience no spread or divergence [ J. Opt. Soc. Am. A4, 651 ( 1987)]. This Communication provides an alternative way of interpreting these results. The approach is based on the McCutchen theorem from which the necessary conditions for a nondiffracting field are derived. This description may be useful in suggesting several different means of synthesizing such fields and in providing a convenient way of estimating their practical limitations. Some examples, inspired by known techniques studied for depth of field enhancement, are briefly mentioned.